Romantic partnerships and the dispersion of social ties

𝐺𝑢

𝐺𝑢 𝐶𝑢𝑣

𝐶𝑢𝑣

𝑑𝑖𝑠𝑝 𝑢, 𝑣 = 𝑑𝑣(𝑠, 𝑡)

𝑠,𝑡∈𝐶𝑢𝑣

𝑑𝑣 𝐶𝑢𝑣

𝑑𝑣(𝑠, 𝑡) = 1, 𝑠 𝑒 𝑡 𝑛𝑜𝑛 𝑠𝑜𝑛𝑜 𝑑𝑖𝑟𝑒𝑡𝑡𝑎𝑚𝑒𝑛𝑡𝑒 𝑐𝑜𝑙𝑙𝑒𝑔𝑎𝑡𝑖

𝑒 𝑛𝑜𝑛 ℎ𝑎𝑛𝑛𝑜 𝑣𝑖𝑐𝑖𝑛𝑖 𝑖𝑛 𝑐𝑜𝑚𝑢𝑛𝑒 𝑖𝑛 𝐺𝑢 𝑜𝑙𝑡𝑟𝑒 𝑎𝑑 𝑢 𝑒 𝑣 0, 𝑎𝑙𝑡𝑟𝑖𝑚𝑒𝑛𝑡𝑖

𝑑𝑖𝑠𝑝 𝑢, 𝑣 𝑒𝑚𝑏 𝑢, 𝑣

𝑑𝑖𝑠𝑝 𝑢, 𝑣

𝑒𝑚𝑏 𝑢, 𝑣

•

𝑛𝑜𝑟𝑚 𝑢, 𝑣 = 𝑑𝑖𝑠𝑝 𝑢, 𝑣 𝑒𝑚𝑏 𝑢, 𝑣

• 𝑛𝑜𝑟𝑚 𝑢, 𝑣

𝑑𝑖𝑠𝑝 𝑢, 𝑣 + 𝑏 𝛼

𝑒𝑚𝑏 𝑢, 𝑣 + 𝑐

𝛼 = 0.61, 𝑏 = 0, 𝑐 = 5

𝐶𝑢𝑣

𝑥𝑣 = 1

𝑥𝑣

𝑥𝑣 = 𝑥𝑤

2 + 2 𝑑𝑣(𝑠, 𝑡)𝑥𝑠𝑠,𝑡∈𝐶𝑢𝑣𝑥𝑡𝑤∈𝐶𝑢𝑣

𝑒𝑚𝑏(𝑢, 𝑣)

𝑥𝑣

𝑟𝑒𝑐(𝑢, 𝑣)